The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network
<p>The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen–Pirjola method for modelling GIC is widely used but was developed when the main a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2022-04-01
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| Series: | Annales Geophysicae |
| Online Access: | https://angeo.copernicus.org/articles/40/205/2022/angeo-40-205-2022.pdf |
| _version_ | 1811299869914038272 |
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| author | R. J. Pirjola D. H. Boteler L. Tuck L. Tuck S. Marsal |
| author_facet | R. J. Pirjola D. H. Boteler L. Tuck L. Tuck S. Marsal |
| author_sort | R. J. Pirjola |
| collection | DOAJ |
| description | <p>The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen–Pirjola method for modelling GIC is widely used but was developed when the main aim was
to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen–Pirjola (LP) method designed to
provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However,
with a network involving multiple voltage levels, many of the nodes are ungrounded, i.e. have infinite resistance to ground, which is numerically inconvenient. The new modified Lehtinen–Pirjola (LPm) method replaces the earthing impedance matrix [<span class="inline-formula"><strong>Z</strong><sup>e</sup></span>] with the corresponding earthing admittance matrix
[<span class="inline-formula"><strong>Y</strong><sup>e</sup></span>] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [<span class="inline-formula"><strong>Y</strong><sup>n</sup></span>] to give a combined matrix ([<span class="inline-formula"><strong>Y</strong><sup>n</sup></span>] <span class="inline-formula">+</span> [<span class="inline-formula"><strong>Y</strong><sup>e</sup></span>]), which is a sparse symmetric
positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages
are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky
decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method
can be easily converted to the LPm method and provides examples of calculations using the LPm method.</p> |
| first_indexed | 2024-04-13T06:43:00Z |
| format | Article |
| id | doaj.art-8058ea3d364d4797b67f6cf3f3217436 |
| institution | Directory Open Access Journal |
| issn | 0992-7689 1432-0576 |
| language | English |
| last_indexed | 2024-04-13T06:43:00Z |
| publishDate | 2022-04-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Annales Geophysicae |
| spelling | doaj.art-8058ea3d364d4797b67f6cf3f32174362022-12-22T02:57:41ZengCopernicus PublicationsAnnales Geophysicae0992-76891432-05762022-04-014020521510.5194/angeo-40-205-2022The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power networkR. J. Pirjola0D. H. Boteler1L. Tuck2L. Tuck3S. Marsal4Geomagnetic Laboratory, Natural Resources Canada, Ottawa, Ontario, CanadaGeomagnetic Laboratory, Natural Resources Canada, Ottawa, Ontario, CanadaGeomagnetic Laboratory, Natural Resources Canada, Ottawa, Ontario, CanadaDefence Research and Development Canada, Dartmouth, Nova Scotia, CanadaObservatori de l'Ebre (OE), Univ. Ramon Llull – CSIC, Horta Alta, 38, 43520 Roquetes, Spain<p>The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen–Pirjola method for modelling GIC is widely used but was developed when the main aim was to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen–Pirjola (LP) method designed to provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However, with a network involving multiple voltage levels, many of the nodes are ungrounded, i.e. have infinite resistance to ground, which is numerically inconvenient. The new modified Lehtinen–Pirjola (LPm) method replaces the earthing impedance matrix [<span class="inline-formula"><strong>Z</strong><sup>e</sup></span>] with the corresponding earthing admittance matrix [<span class="inline-formula"><strong>Y</strong><sup>e</sup></span>] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [<span class="inline-formula"><strong>Y</strong><sup>n</sup></span>] to give a combined matrix ([<span class="inline-formula"><strong>Y</strong><sup>n</sup></span>] <span class="inline-formula">+</span> [<span class="inline-formula"><strong>Y</strong><sup>e</sup></span>]), which is a sparse symmetric positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method can be easily converted to the LPm method and provides examples of calculations using the LPm method.</p>https://angeo.copernicus.org/articles/40/205/2022/angeo-40-205-2022.pdf |
| spellingShingle | R. J. Pirjola D. H. Boteler L. Tuck L. Tuck S. Marsal The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network Annales Geophysicae |
| title | The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| title_full | The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| title_fullStr | The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| title_full_unstemmed | The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| title_short | The Lehtinen–Pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| title_sort | lehtinen pirjola method modified for efficient modelling of geomagnetically induced currents in multiple voltage levels of a power network |
| url | https://angeo.copernicus.org/articles/40/205/2022/angeo-40-205-2022.pdf |
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